Write the explicit equation for this sequence. 4, 7.5, 11, 14.5,
18...

Work Shown:

a = 4 is the first term

d = 3.5 is the common difference (we add this to each term to get the next term)

f(n) = nth term of arithmetic sequence

f(n) = a + d*(n-1)

f(n) = 4 + 3.5(n-1)

f(n) = 4 + 3.5n - 3.5

f(n) = 3.5n + 0.5

As a check, we could plug in n = 1 to get

f(n) = 3.5n+0.5

f(1) = 3.5(1)+0.5

f(1) = 4

Showing that 4 is the first term. Now let's try n = 2

f(n) = 3.5n+0.5

f(2) = 3.5(2)+0.5

f(2) = 7.5

Which matches with the sequence also.

I'll let you confirm the other terms.

the ratio of balloons to tables is 5: 2 and the constant variation is 5.

the equation is y=5x